John B, (01)
I agree that a logic that provides support for nested contexts
(or whatever anyone wants to call them) is important. But as
Pat Hayes has said many times, the word 'context' has become
so ambiguous that nobody knows what it means. My recommendation
is very simple: (02)
1. Provide a container (a box or some other kind of marker)
that delimits whatever anyone wants to say about the
so-called context. (03)
2. Make it possible to refer to the box by a name or variable
assigned to the box and to make any kinds of statements
outside the box about information inside the box. (04)
3. Make no fixed assumptions about a "context logic" for how
the information inside the box is related to anything
outside the box. But allow any version anyone might like
to define to be specified by axioms outside the box. (05)
4. Allow the boxes to be nested to any depth. And let people
define axioms for how information at various levels is
related. (06)
Conceptual graphs have had such boxes since 1976, and the word
I use for a box is "context". Although people talk about contexts
in various ways, I have found that such a box mechanism can usually
be used to characterize what they say about their contexts. I won't
say "always" because I haven't examined every proposal, but this
kind of notation seems to be adequate to cover the mechanisms used
in natural languages. (07)
The IKL extensions to CL can be mapped to the CG boxes, but IKL
provides a more specialized semantics, and Pat has said that more
study is required to ensure that the semantics is sound. The
IKRIS Context Logic (ICL) adds more axioms to the IKL base, and
Pat has been even more negative about ICL. (08)
My attitude toward axioms is to enforce the refrigerator policy: (09)
"When in doubt, throw it out." (010)
In other words, if there is any disagreement about what axioms
should be included in the common core, then exclude any of them
from the common core that raise any objections. But allow anybody
to add any kind of special-case axioms they prefer. If this
policy leaves the refrigerator empty, that's a good way to start.
People can add whatever they need as they choose. (011)
JB> Would it be simpler for a human if this was visible graphically?
> And does it make any difference to a machine? Do you think there
> is any parallel in automated processors of the advantages to humans
> of graphical reasoning? (012)
In designing conceptual graphs, I observe the following principles: (013)
1. Every CG construct must have a smooth translation to natural
languages. (014)
2. Every CG construct must have a formal mapping to predicate
calculus (possibly with some reasonable extensions). (015)
3. The graphical display form should be easily readable by
humans. (016)
4. The formal operations should be few, simple, general, and
sufficient to support the kinds of reasoning performed with
other versions of logic. (017)
Principles #2 and #4 are necessary to make CGs suitable for formal
reasoning and computational efficiency. Principle #1 is necessary
to make CGs suitable as an intermediate notation for NL semantics.
Principles #1 and #3 are necessary to make them humanly readable. (018)
Those four principles, by themselves, do not uniquely determine
the structure of CGs. Additional ideas have come from many
different sources -- primarily various kinds of logic, NL semantics,
AI research, and Peirce's writings on existential graphs. (019)
Following is an article that discusses contexts in general and
proposes nested graph models (NGMs) as a basis for the semantics: (020)
http://www.jfsowa.com/pubs/laws.htm
Laws, Facts, and Contexts (021)
John Sowa (022)
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